The Chen-Luo test in case of heteroscedasticity

Chen and Luo (2004, Comm. Statist. Simulation Comput. 33, 1007-1020) presented a modification of the Wilcoxon-Mann-Whitney test that can be less conservative than the original test. The results shown here indicate that the possible power advantage of the modification is solely due to its being less conservative. Because the modified statistic is variance adjusted using a variance estimator based on the empirical data situation independent of the null hypothesis, the test may be useful in case of heteroscedasticity. However, it is demonstrated here that the modified test can be much more anticonservative than the Wilcoxon-Mann-Whitney test when the population means are identical, but the population variances differ. Therefore, the modified test cannot be recommended for the nonparametric Behrens-Fisher problem. Possible approaches in that case are the Brunner-Munzel test and Cliff's method.

[1]  Xiaohui Luo,et al.  Some Modifications on the Application of the Exact Wilcoxon–Mann–Whitney Test , 2004 .

[2]  Ronald H. Randles,et al.  On Neutral Responses (Zeros) in the Sign Test and Ties in the Wilcoxon–Mann–Whitney Test , 2001 .

[3]  E. Brunner,et al.  The Nonparametric Behrens‐Fisher Problem: Asymptotic Theory and a Small‐Sample Approximation , 2000 .

[4]  S Ogenstad.  The use of generalized tests in medical research. , 1998, Journal of biopharmaceutical statistics.

[5]  Werner Baumgartner,et al.  A Nonparametric Test for the General Two-Sample Problem , 1998 .

[6]  C. W. Coakley,et al.  Versions of the Sign Test in the Presence of Ties , 1996 .

[7]  M. Neuhäuser.  Two-sample tests when variances are unequal , 2002, Animal Behaviour.

[8]  R. Bergmann,et al.  Different Outcomes of the Wilcoxon—Mann—Whitney Test from Different Statistics Packages , 2000 .

[9]  R. Wilcox.  Introduction to Robust Estimation and Hypothesis Testing , 1997 .

[10]  J Singer,et al.  A simple procedure to compute the sample size needed to compare two independent groups when the population variances are unequal , 2001, Statistics in medicine.

[11]  Edgar Brunner,et al.  A studentized permutation test for the non-parametric Behrens-Fisher problem , 2007, Comput. Stat. Data Anal..

[12]  Jeno Reiczigel,et al.  A Bootstrap Test of Stochastic Equality of Two Populations , 2005 .

[13]  Irwin Guttman,et al.  Statistical inference for Pr(Y < X): The normal case , 1986 .

[14]  J. L. Rasmussen.  Analysis of Likert-scale data: A reinterpretation of Gregoire and Driver. , 1989 .

[15]  E. Kasuya.  Mann–Whitney U test when variances are unequal , 2001, Animal Behaviour.

[16]  Markus Neuhäuser,et al.  Exact tests based on the Baumgartner-Weiß-Schindler statistic—A survey , 2005 .

[17]  N. Cliff.  Dominance statistics: Ordinal analyses to answer ordinal questions. , 1993 .

[18]  Markus Neuhäuser,et al.  COMPARING PARASITE NUMBERS BETWEEN SAMPLES OF HOSTS , 2004, The Journal of parasitology.

[19]  Roy C. Milton,et al.  Rank order probabilities;: Two-sample normal shift alternatives , 1970 .

[20]  R. Wilcox.  Applying Contemporary Statistical Techniques , 2003 .

[21]  András Vargha,et al.  Comparing several robust tests of stochastic equality with ordinally scaled variables and small to moderate sized samples. , 2002, Psychological methods.